Bounded Curvature Without Eigenanalysis

Malcolm A. Sabin, Thomas J. Cashman, Ursula Augsdörfer, Neil A. Dodgson

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This paper provides an alternative insight, based on the use of second divided differences, and applies it to three familiar schemes. A single concept is shown to work in three different contexts. In each case a bounded curvature variant results, with a very simple and elegant implementation.
Original languageEnglish
Title of host publicationMathematics of Surfaces XII
Subtitle of host publicationMathematics of Surfaces 2007
EditorsR. Martin, M. Sabin, J. Winkler
PublisherSpringer
Pages391-411
ISBN (Electronic)978-3-540-73843-5
ISBN (Print)978-3-540-73842-8
DOIs
Publication statusPublished - 4 Sep 2007
Event2007 IMA International Conference on Mathematics of Surfaces: Mathematics of Surfaces 2007 - Sheffield, United Kingdom
Duration: 4 Sep 20076 Sep 2007

Publication series

NameLecture Notes in Computer Science
Volume4647

Conference

Conference2007 IMA International Conference on Mathematics of Surfaces
CountryUnited Kingdom
CitySheffield
Period4/09/076/09/07

Fingerprint

Curvature
Subdivision Scheme
Divided Differences
Mask
Alternatives
Context
Concepts

Cite this

Sabin, M. A., Cashman, T. J., Augsdörfer, U., & Dodgson, N. A. (2007). Bounded Curvature Without Eigenanalysis. In R. Martin, M. Sabin, & J. Winkler (Eds.), Mathematics of Surfaces XII : Mathematics of Surfaces 2007 (pp. 391-411). (Lecture Notes in Computer Science; Vol. 4647). Springer. https://doi.org/10.1007/978-3-540-73843-5_24

Bounded Curvature Without Eigenanalysis. / Sabin, Malcolm A. ; Cashman, Thomas J. ; Augsdörfer, Ursula; Dodgson, Neil A. .

Mathematics of Surfaces XII : Mathematics of Surfaces 2007. ed. / R. Martin; M. Sabin; J. Winkler. Springer, 2007. p. 391-411 (Lecture Notes in Computer Science; Vol. 4647).

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Sabin, MA, Cashman, TJ, Augsdörfer, U & Dodgson, NA 2007, Bounded Curvature Without Eigenanalysis. in R Martin, M Sabin & J Winkler (eds), Mathematics of Surfaces XII : Mathematics of Surfaces 2007. Lecture Notes in Computer Science, vol. 4647, Springer, pp. 391-411, 2007 IMA International Conference on Mathematics of Surfaces, Sheffield, United Kingdom, 4/09/07. https://doi.org/10.1007/978-3-540-73843-5_24
Sabin MA, Cashman TJ, Augsdörfer U, Dodgson NA. Bounded Curvature Without Eigenanalysis. In Martin R, Sabin M, Winkler J, editors, Mathematics of Surfaces XII : Mathematics of Surfaces 2007. Springer. 2007. p. 391-411. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-540-73843-5_24
Sabin, Malcolm A. ; Cashman, Thomas J. ; Augsdörfer, Ursula ; Dodgson, Neil A. . / Bounded Curvature Without Eigenanalysis. Mathematics of Surfaces XII : Mathematics of Surfaces 2007. editor / R. Martin ; M. Sabin ; J. Winkler. Springer, 2007. pp. 391-411 (Lecture Notes in Computer Science).
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